Turbo engines also tend to weigh less than naturally aspirated engines with the same power output.

I think the only reason we're not seeing more is just due to lack of development. If you look back a few years ago, the new turbo engines coming out weren't at all optimized for fuel efficiency. Mitsubishi, Subaru, Mazda - none of the 2000's generation engines were particularly clean or thrifty. Interestingly, Subaru's latest 'base' engine that they introduced to improve efficiency is NA.